This paper explores the potential of the intelligent reflecting surface (IRS) in realizing multi-user concurrent communication and localization, using the same time-frequency resources. Specifically, we propose an IRS-enabled multi-user integrated sensing and communication (ISAC) framework, where a distributed semi-passive IRS assists the uplink data transmission from multiple users to the base station (BS) and conducts multi-user localization, simultaneously. We first design an ISAC transmission protocol, where the whole transmission period consists of two periods, i.e., the ISAC period for simultaneous uplink communication and multi-user localization, and the pure communication (PC) period for only uplink data transmission. For the ISAC period, we propose a multi-user location sensing algorithm, which utilizes the uplink communication signals unknown to the IRS, thus removing the requirement of dedicated positioning reference signals in conventional location sensing methods. Based on the sensed users' locations, we propose two novel beamforming algorithms for the ISAC period and PC period, respectively, which can work with discrete phase shifts and require no channel state information (CSI) acquisition. Numerical results show that the proposed multi-user location sensing algorithm can achieve up to millimeter-level positioning accuracy, indicating the advantage of the IRS-enabled ISAC framework. Moreover, the proposed beamforming algorithms with sensed location information and discrete phase shifts can achieve comparable performance to the benchmark considering perfect CSI acquisition and continuous phase shifts, demonstrating how the location information can ensure the communication performance.